Solve for $p$, $ \dfrac{8}{16p - 20} = -\dfrac{5p - 6}{4p - 5} - \dfrac{1}{20p - 25} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $16p - 20$ $4p - 5$ and $20p - 25$ The common denominator is $80p - 100$ To get $80p - 100$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ \dfrac{8}{16p - 20} \times \dfrac{5}{5} = \dfrac{40}{80p - 100} $ To get $80p - 100$ in the denominator of the second term, multiply it by $\frac{20}{20}$ $ -\dfrac{5p - 6}{4p - 5} \times \dfrac{20}{20} = -\dfrac{100p - 120}{80p - 100} $ To get $80p - 100$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ -\dfrac{1}{20p - 25} \times \dfrac{4}{4} = -\dfrac{4}{80p - 100} $ This give us: $ \dfrac{40}{80p - 100} = -\dfrac{100p - 120}{80p - 100} - \dfrac{4}{80p - 100} $ If we multiply both sides of the equation by $80p - 100$ , we get: $ 40 = -100p + 120 - 4$ $ 40 = -100p + 116$ $ -76 = -100p $ $ p = \dfrac{19}{25}$